ESTIMATION OF AVERAGE GRADIENT 363 



For the purposes of this study, the average (per kilometer) gradient of 

 the first kilometer of the atmosphere is the only prediction parameter 

 used which will require upper air measurements. The average 1 km 

 gradient, 



AN = Ni - Ns, (8.45) 



where A'^i is refractivity at 1 km above the surface, was selected because 

 climatological summaries, as in chapter 4, can be used to estimate the 

 height error when meteorological measurements are unobtainable. 



8.4.6. Calculation and Correlation of Height Errors 



Bean, Gaboon, and Thayer [18] selected refractive index profiles, deter- 

 mined from radiosonde observations at 13 climatically distinct locations, 

 which represent a wide variety of mutually exclusive profile types. The 

 ray paths at arrival angles varying from 0° to near 90° were determined 

 for each profile by numerical evaluation of (8.29) through (8.33) using 

 methods similar to those described by Bean and Thayer [1]. The height 

 errors were calculated with (8.33) and (8.34) at selected height intervals 

 of 70,000 ft for each ray path. Newton's method of interpolation was 

 used to determine height errors for fixed ground distances to 150 mi. The 

 limits of height and distance were chosen to extend beyond the current 

 needs in terminal air traffic control, but are sufficiently restricted to allow 

 some of the previous assumptions. 



The prediction parameters, N s, Go, and AA'^, were obtained from each 

 of the refractive index profiles. Linear and multiple regression analysis 

 were employed to obtain least squares estimates of the height error at 

 each height and distance for each prediction parameter and for various 

 combinations of the parameters. 



8.4.7. Estimation of the Average Gradient 



Based on the correlations the following forms, suggested by (8.43), were 

 selected for approximating g: 



?■ = J^^fniha), (8.46) 



92 = ^/2l(/la) -^-—-Mha) (8.47) 



or 



^3 = ^Mha) + ^Mha) + -J^Miha) (8.48) 



depending upon the availability of Go and AA'^. 



